Anomalous Low Frequency Dispersion Research Articles

Evidence of a third kind of Johnscher’s like universal dielectric response

Polymer/metal composites (PMC) comprising of polyvinylidene fluoride/nanocrystalline nickel with varying volume fractions of nickel ([Formula: see text]) prepared under cold press show an insulator to metal transition (IMT) at percolation threshold ([Formula: see text]). The two kinds of generalized Johnscher’s universal dielectric response (UDR) laws on both sides of IMT hold good, while for the percolative sample, none of the two laws hold good. Neither the concept of dipolar relaxation nor anomalous low frequency dispersion stands valid for [Formula: see text], while a completely different, neutral and competing electrical behavior is observed over the entire range of frequencies. The emerged third kind of Johnscher’s like UDR for [Formula: see text] is observed and the relaxation law has been formulated as the ratio of imaginary and real parts of dielectric constant remains constant over the entire range of frequency starting from dc to any higher frequency. The value of the constant is attributed to depend on the PMC, the dielectric constant of the polymer, the differences of conductivity and fractions of the components of the PMC and also on their connectivity arising due to the difference of their process conditions. The emerged unique dielectric relaxation consists of multiple relaxations arising due to the combination of other relaxations (arising due to the two different types of species) present in the sample, [Formula: see text]. This novel material may be suitable for certain specific applications in electrical and electronics engineering.

New DC conductivity spectra of Zn–Al layered double hydroxide (Zn–Al–NO3–LDH) and its calcined product of ZnO phase

Zn–Al–NO3–LDH nanostructure was synthesized via the coprecipitation method at molar ratio Zn2+/Al3+ = 4 and pH = 7. The resultant sample was thermally treated at calcined temperatures of 50, 100, 150, 200, 250 and 300 °C. The layered structure of the Zn–Al–NO3–LDH samples was stable below the calcination temperature 200 °C as shown in powder X-ray diffraction (PXRD) patterns of calcined samples. The calcination products showed a collapse of LDH structure and ZnO phase was formed at 200 °C and above. The dielectric spectroscopy of LDH was explained using anomalous low frequency dispersion (ALFD) due to the low mobility of LDH carriers. The conductivity spectra of LDH can be theoretically described according to the effective phase within the calcination products of LDH. In the comparison with previously researches, this study presented higher values of DC conductivity for all studied samples.

Synthesis and Optimization of Electric Conductivity and Thermal Diffusivity of Zinc-Aluminum Hydroxide (Zn–Al–NO3–LDH) Prepared at Different pH Values

Zn–Al–NO3–LDH was synthesized using the co-precipitation method at different pH values of 6, 7, 8, 9 and 10 with Zn2+/Al3+ = 4. The structural, textural and morphological properties of samples were studied. All prepared samples were mesoporous materials. The dielectric response of Zn–Al–NO3–LDH samples can be described by anomalous low frequency dispersion (ALFD). Thermal diffusivity of samples has been measured as a function in in situ temperature at range 27 – 210°C. The optimized electrical conductivity and thermal diffusivity has been found with the synthesized Zn–Al–NO3–LDH sample at pH 8.

Influence of sodium dodecyl sulfate concentration on the photocatalytic activity and dielectric properties of intercalated sodium dodecyl sulfate into Zn–Cd–Al layered double hydroxide

Sodium dodecyl sulfate (SDS) has been successfully intercalated into Zn–Cd–Al–LDH precursor with different SDS concentrations (0.2, 0.3, 0.4, 0.5 and 1molL−1) using the coprecipitation method at (Zn2++Cd2+)/Al3+ molar ratio of 13 and pH 8. The structural, morphological, texture and composition properties of the synthesized (Zn–Cd–Al–LDH–DS) nanostructure were investigated using powder X-ray diffraction (PXRD), scanning electron microscope (SEM), thermogravimetric analysis (TGA) and Fourier transform infrared (FT-IR), respectively. The photocatalytic activity of these materials was developed by increasing the concentration of intercalated SDS. The absorbance spectra have been used to detect an anion in the LDH interlayer before and after the intercalation process, which confirmed the presence of the dodecyl sulfate (DS−) anion into LDH gallery after intercalation. The anomalous low frequency dispersion (ALFD) has been used to describe the dielectric response of Zn–Cd–Al–LDH–DS nanostructure using the second type of universal power law. At low frequency, the polarization effect of electrodes caused the rising in dielectric constant and loss values. An important result of the dielectric measurements is the calculated dc conductivity values, which are new in dielectric spectroscopy of LDH materials. An important result of the electron spin resonance (ESR) spectra exhibited the successful intercalation of DS molecule into LDH gallery. The g-factor value was affected by the SDS concentration which indicated changes to the environment around the DS molecule in LDH interlayer.

Dielectric spectroscopy of polymer-metal composites across the percolation threshold

Polymer (polar/nonpolar)/metal composites (PMC) were prepared under different process conditions. In polar PMC, dipolar relaxation plays a predominant role below percolation threshold (fc) and anomalous low frequency dispersion (ALFD) becomes dominant above fc while ALFD is the only likely possibility for nonpolar PMC above fc. The magnitude of relaxation exponents "m", "p" and "n", evaluated from the experimental results using Jonscher's universal dielectric response (JUDR) laws, falls within the universal limit ~ [0, 1] with additional feature of strong dependence on volume fraction of conductor (f con ). The decrease in the relaxation exponent "m" with an increase of f con is directly linked with decrease in the number of dipoles of the polymer in the composite and is accompanied by a distribution of relaxation time due to increased heterogeneity of the system. The magnitude of the relaxation exponent "n" decreases at fc, due to the prevalence of Maxwell–Wagner–Sillar polarization contributed by uncorrelated electrons.

Characterizing epoxy composites filled with carbonaceous nanoparticles from dc to microwave

We have used several methods to measure the effective complex permittivity of epoxy composites filled with carbonaceous (carbon black, single-walled carbon nanotube, and multi-walled carbon nanotube) over nine decades of frequency. The composite samples were fabricated by shear mixing. The spectral analysis of permittivity of these nanocomposites is in good agreement with Jonscher's modelling. We point out, taking these examples, that the experimental frequency dependence of the effective permittivity has a range of interesting properties. The likely transport mechanisms responsible for the dielectric relaxation in these samples can be modelled by the dipolar relaxation and anomalous low-frequency dispersion below and above percolation, respectively.

In situ dielectric measurements of Zn–Al layered double hydroxide with anionic nitrate ions

Zn–Al–NO3–layered double hydroxide (Zn–Al–NO3–LDH) was prepared by the co-precipitation method with a ratio of Zn/Al = 4 and at a constant pH of 7. Powder XRD patterns showed the characteristic peaks of layered structure of the LDH sample. Thermogravimetric analysis (TGA) and infrared spectra of the sample were investigated. Because of the existence of water molecules and anionic NO3− in the interlayer of the LDH, the in situ dielectric spectroscopy of the LDH can be described by an anomalous low frequency dispersion using the second type of Universal Power Law. Novel measurements of activation energy of LDH have been obtained at five different frequencies. The energy value increased from 0.05 eV at 1 MHz to 0.37 eV at 134 Hz. The conductivity spectra of sample were studied as a function in temperature of the in situ measurements. The ionic conductivity (dc) of LDH increased as the in situ temperature increased.

Zn–Al layered double hydroxide prepared at different molar ratios: Preparation, characterization, optical and dielectric properties

The co-precipitation method was used to prepare Zn–Al–NO3-LDH at different Zn2+/Al3+ molar ratios (2, 3, 4, 5 and 6) and pH value of 7.5. The structure, textural, composition and morphological properties were investigated using powder X-ray diffraction (PXRD), thermogravimetric analysis (TGA), Fourier transform infrared (FT-IR) and scanning electron microscope (SEM), respectively. The crystallinity of LDH samples were found to improve as molar ratio decreased which is attributed to the distortion of the hydroxide layers networks of the LDH crystal by the larger difference in ionic radii of Zn2+ and Al3+. The optical band gap energy of LDH samples were evaluated using absorbance data from UV–Vis–NIR Diffuse reflectance spectroscopy. Band gaps were affected by the variation of the Zn2+/Al3+ molar ratio is due to the formation of the low crystalline phases (ZnO and ZnAl2O4). The water molecules and anionic NO3− in the LDH interlayer were responsible for the generation of the dielectric response. This response can be described by an anomalous low frequency dispersion using the second type of Universal Power Law. The dominance of ZnO dipoles and charge carriers (NO3− ions) in the dielectric relaxation increases with the increasing molar ratio.

Thermal, optical and dielectric properties of Zn–Al layered double hydroxide

Zn–Al–NO 3–layered double hydroxide (Zn–Al–NO 3–LDH) was prepared by the co-precipitation method at a constant pH of 7 and a ratio of Zn/Al = 4. A thermal treatment was performed for LDH at various temperatures. Powder XRD patterns showed that the layered structure of the LDH samples was stable below 200 °C, which was also confirmed by thermogravimetric (TGA) and differential thermal (DTA) analyses. Infrared spectra of the samples showed the characteristic peaks of LDH, and changes of these peaks were observed when thermal treatment was performed above 150 °C. Diffuse reflectance spectroscopy of the samples showed more than one energy gap at calcination temperatures below200 °C. In samples calcined at 200 °C and above only one energy gap was observed at approximately 3.3 eV. The photocatalytic activity was found to increase with the increase of the ZnO crystal size, which can be achieved by increasing the calcination temperature of the samples. Because of the presence of water molecules and anionic NO 3 − in the interlayer of the LDH, the dielectric response of the calcined LDH can be described by an anomalous low frequency dispersion using the second type of Universal Power Law for calcination temperatures below 200 °C. The dielectric response of the calcined LDH above 150 °C displays the dielectric relaxation behaviour of ZnO because of the formation of a ZnO phase in the LDH within this temperature range.

Dielectric relaxation in carbon black-epoxy composite materials

Filled polymers have been a fertile area for modeling studies of microwave dynamics, percolation, and elasticity network formation to mention but a few. To better understand the basic concepts relevant to wave transport in filled polymers, an experimental validation is paramount for theories that predict the dielectric response and, hence, the polarization mechanisms of these heterostructures. Reproducible measurements of the effective complex permittivity, at ambient temperature, are reported in the frequency range of 200 Hz–15 MHz for series of carbon black (CB)-epoxy composites that provide a detailed and quantitative characterization of the dielectric relaxation behavior. We provide observational evidence showing that dipolar relaxation and anomalous low-frequency dispersion are likely the transport mechanisms in these samples below and above percolation, respectively. The various fractional exponents of the power-law decay of these spectral models are analyzed, and Hill plots can be used to rationalize the effective complex permittivity observations for these series of samples. Our results have important implications for designing and optimizing engineered CB/polymer materials for a broad spectrum of engineering applications, e.g., solid broadband tissue simulant materials and electromagnetic absorbers.

Dielectric relaxation in slightly hydrated bovine tendon collagen

With an aim to reveal the mechanism of water–protein interaction from the dielectric response of a model fibrous protein, the dielectric constant ε′ and loss factor ε″ have been measured in air dried and vacuum dried samples of bovine tendon collagen in the frequency range 30 Hz–3 MHz and temperature range 30–200 °C. An anomalous low frequency dispersion (LFD) and an intermediate frequency strong α-dispersion peak were the two main dielectric responses observed in the air dried sample. The LFD followed the fractional power law of frequency while the α-dispersion conformed to the Cole–Cole modified Debye equation. These dispersions, respectively, have been attributed to percolation of protons between and within the clusters of hydrogen bonded water molecules bound to polar or ionizable protein components. In the vacuum dried sample, however, a very weak high frequency α2-dispersion peak was observed, which was hidden below the strong α-dispersion in the air dried sample. This peak may be attributed to reorientation of polar components of the collagen molecule.Temperature dependence of the dielectric data shows release of bound water as a four-step process with discrete peaks at 50, 90, 125 and 160 °C. These peaks have been attributed to the onset of the release of adsorbed surface water, water bound to exposed polar sites, water bound to internal polar sites and very strongly bound structural water, respectively.

Signs of low frequency dispersions in disordered binary dielectric mixtures (fifty–fifty)

Dielectric relaxation in disordered dielectric mixtures is presented by emphasizing the interfacial polarization. The obtained results coincide with and cause confusion with those of the low frequency dispersion behaviour. The considered systems are composed of two phases on two-dimensional square and triangular topological networks. We use the finite element method to calculate the effective dielectric permittivities of randomly generated structures. The dielectric relaxation phenomena together with the dielectric permittivity values at constant frequencies are investigated, and significant differences of the square and triangular topologies are observed. The frequency dependent properties of some of the generated structures are examined. We conclude that the topological disorder may lead to the normal or anomalous low frequency dispersion if the electrical properties of the phases are chosen properly, such that for ‘slightly’ reciprocal mixture—when σ1 ≫ σ2, and ϵ1 < ϵ2-normal, and while for ‘extreme’ reciprocal mixture—when σ1 ≫ σ2, and ϵ1 ≪ ϵ2-anomalous low frequency dispersions are obtained. Finally, comparison with experimental data indicates that one can obtain valuable information from simulations when the material properties of the constituents are not available and of importance.

A percolation cluster model of the temperature dependent dielectric properties of hydrated proteins

This study investigates the temperature dependence of the low frequency dielectric properties (0.1 Hz–1 MHz) of hydrated globular proteins (namely, ovalbumin, lysozyme and pepsin). The study aims to reveal the mechanisms of water–protein interaction from the dielectric response of these model proteins. Two principle dielectric responses were observed for each hydrated protein, namely, an anomalous low frequency dispersion and a dielectric loss peak at higher frequency (called the ε3 dispersion). The low frequency response conformed to a fractional power low of frequency, while the higher frequency response conformed to a Davidson–Cole model. The strength of both processes reached a maximum at a certain temperature within the experimental temperature range. This temperature is referred to as the percolation threshold (PT) and is thought to be associated with the percolation of protons between hydrogen-bonded water molecules. The relaxation times of the ε3 dispersion conformed to Arrhenius behaviour at temperatures below the PT, from which an activation energy (ΔH) could be calculated. This activation energy is thought to be a measure of the concentration of available charged sites through which proton transport is facilitated. The structural fractal dimension in the hydrated protein system was also calculated, and enabled the approximation of the pathway for charge percolation in the protein matrix.

Anomalous diffusion of defects in rutile-titanium dioxide: correlation between ac conductivity and defect structures

This work is concerned with the measurement of conductivity σ( ω), and also permittivity ε( ω), in samples of TiO 2 of rutile structure. The electrical response exhibits universal behavior in the form of power-law dependences on frequency, which was labeled as anomalous low-frequency dispersion. In the used measuring conditions, charge transport is due to the diffusion of ionic defects of the bulk material. Two crossover frequencies were found that signal the transition between different diffusing regimes. One of them is restricted to small, structural size regions ( ξ∼5 Å), in the same way as localized motion of cations commonly reported for ion-containing glasses. The second diffusing regime is confined inside the regions of nanometer scale ( ξ′∼5 nm), which is interpreted in terms of the correlated charge motions in the observed clusters of defects (crystallographic share planes). Therefore, this study highlights the correlation between electrical measurement and structural properties.

Development of a remote electrode system for monitoring the water content of materials inside a glass vial.

This article explores the use of a remote electrode dielectric measurement system to monitor the water content of hydrated ovalbumin inside a glass vial. The intrinsic dielectric properties of hydrated ovalbumin were characterized first using conventional parallel plate electrodes. The second stage was to simulate a remote electrode measurement by placing nonconductive, nondispersive polyethylene films between the sample and electrodes. Finally, a study on the dielectric measurement of ovalbumin contained in a 10 ml glass vial was undertaken with the electrodes external to the glass vial. The dielectric behavior of hydrated ovalbumin was characterized by charge transfer (i.e., protons) in the hydrogen bonded network of water molecules in the bulk sample. The mechanism was identified as an anomalous low-frequency dispersion and a dielectric loss peak (epsilon3). The dielectric relaxation time, tau3, of the epsilon3 dispersion was especially sensitive to water content. Moreover, a good correlation (R2 = 93%) was observed between relaxation times tau3 obtained from measurements using conventional parallel plate electrodes and the remote electrode system. Dielectric measurements using remote electrodes attached to a glass vial are therefore applicable for the in situ measurement of water content in materials. The application of this technology to the determination of the lyophilization end point is suggested.

Fractal analysis of anomalous low-frequency dispersion inX2BaCuO5compounds(X=La–Y)

The anomalous low-frequency dispersion process observed in perovskite ceramics ${(X}_{2}{\mathrm{BaCuO}}_{5},X=\mathrm{La}--\mathrm{Y})$ is described by a fractal model. The interpretation is given in terms of the Dissado-Hill-Jonscher theory and is based on a cluster description of the structural ordering and fluctuation in carrier-dominated dielectrics. The relationship of the mechanism to that of power-law noise in electrical systems is identified and its dynamical and structural interpretation explored. Particular features of several ceramics related to superconductor compounds are described.

Dielectric response and a.c. conductivity of synthetic dopa-melanin polymer

The dielectric spectra of dopa-melanin have been examined over the wide frequency range 100 Hz–1000 MHz at room temperature. Synthetic dopa-melanin was obtained by oxidative polymerization of L-3,4-dihydroxyphenylalanine. The purpose of the present study was to characterize polarization effects, the electrical conduction mechanism and structural arrangement of the units taking part in these processes as a basis for future biological applications. Real and imaginary components of the dielectric permittivity show an anomalous low-frequency dispersion. Values of the power-law exponents were interpreted in terms of the cluster model of potentially mobile charges and the structural arrangement of molecular units in melanin. The fractal circuit model (self-similar branched porous electrode system) was found to be equivalent to the cluster model in the description of the dielectric response in melanin. It has been shown that relations between cluster model parameters p and n, and fractal dimensionalities of melanin, are fulfilled very well. The presented results support the earlier findings based on d.c. conductivity measurements, that charge hopping is the main conduction mechanism, which contributes to the dielectric polarization in the low-frequency region. Dielectric spectra at frequencies above 10MHz show small β-relaxation features due to molecular polar segments and water molecules bound to melanin. © 1998 Kluwer Academic Publishers

Anomalous low frequency dispersion and dielectric relaxation in the layered intercalated compounds Cd0.75PS3A0.5(H2O) [A=K, Cs

The dielectric response in the layered Cd0.75PS3A0.5(H2O) [A=K, Cs] in which hydrated alkali cations reside in the interlamellar space, have been investigated as a function of frequency and temperature. In these materials the layers are electrically insulating, the alkali ions immobile and the electrical response due to the intercalated water molecules. The dielectric behavior shows two phenomena, an anomalous dispersion of the complex dielectric susceptibility at low frequencies and a dielectric relaxation at higher frequencies. At low frequencies the complex dielectric permittivity of both compounds show a power law dispersion with a transition to a smaller exponent above a crossover frequency, ωc. It was found that although ωc shifts to higher frequency with increasing temperature the magnitude of the complex permittivity at the crossover frequency showed no variation. The loss peak showed a similar shift to higher frequencies with temperature. The dielectric relaxation showed increasing departure from an ideal Debye response with temperature. The results have been rationalized by considering the intercalated water molecules as forming a H-bonded network structure. The dielectric behavior is described in the context of a percolation structure for this network. The anomalous low frequency dispersion arises due to imperfect transport on this structure and the dielectric loss due to the fact that the water molecules possess a permanent dipole moment.

Structure order-disorder and dielectric response in perovskite-related SrO-Fe2O3-Nb2O5 system: The oxygen-deficient composition Sr(Fe1−xNbx)O2.5+y (x=0.17, 0.25, 0.50)

Microstructures of materials with composition Sr(Fe1−xNbx)O2.5+y (x=0.17, 0.25, 0.50) have been investigated by powder x-ray diffraction (XRD) and transmission electron microscopy (TEM) examinations. XRD data for ceramic samples annealed under different P(O2) conditions could be indexed to a cubic perovskite. Superlattice diffraction spots have been observed by TEM investigation for the samples which were re-equilibrated by a subsequent annealing in a reducing atmosphere. A microdomain model is proposed to describe the observed phenomena. According to the model, the structure of reduced Sr(Fe1−xNbx)O2.5+y with x=0.17, 0.25 is considered to be a result of disordered intergrowth between brownmillerite-type Sr2Fe2O5 domains and perovskite-type Sr(Fe0.5Nb0.5)O3 domains. Brownmillerite-type domains are formed because of vacancy ordering. The order is extremely short ranged. Electron diffraction patterns constructed in terms of this microdomain model agree well with the observed results. The order-disorder transition can be altered by varying ambient oxygen partial pressures. For both ordered and disordered samples the frequency-domain dielectric response as a function of temperature is reported. Directly measured complex conductivity Y(ω) has been transformed by Kramers–Kronig relations in order to subtract the disturbances of G(0) and C(∞). The transformed temperature dependences have been further normalized and re-expressed in the form of master curves. For all the samples measured, the frequency-domain dielectric response deviates from the Debye model but follows the so-called universal power law behavior. The dielectric spectra for the samples in which brownmillerite-type ordering is identified show an anomalous low-frequency dispersion, while for the disordered samples, the relaxation behavior with a loss peak is observed. The variation of spectra shape with composition indicates that increasing Nb content tends to weaken the cooperative many-body interactions and causes the dielectric behavior to approach the Debye model.

Strong low-frequency electrical dispersion in microemulsions

Microemulsions have drawn considerable technological and scientific interest due to their peculiar properties. The time-domain response and the anomalous low-frequency dispersion of electrical conductivity and of dielectric permitivity over a range of temperatures (15 ≤ T ≤ 40°C) and compositions for several microemulsions has been obtained. Time-domain and frequency responses were analyzed in the framework of universal laws. Interpretation of the data in the light of the current theories has been discussed.